Comments on a floating-point version of Nordsieck’s scheme for the numerical integration of differential equations

One of the important problems in numerical analysis which arises in scientific and engineering research is that of numerical integration of a system of differential equations. Because of the frequency with which this problem occurs, it is valuable to have a general-purpose numerical scheme with which the integration of a large class of differential equations can be reliably performed. One numerical scheme which is useful as such a general-purpose method, and well adapted for efficient use with digital computers, has been proposed by A. Nordsieck [1], [2]. This scheme is designed to solve a system of first-order equations,